Question

The measure of the acute angles of a right triangle are (2x -3) and (3x-7). What is the measure of the smallest angle in the triangle

Answer 1

Answer:

given

it is a right angle triangle

so one of the angle is 90

(2x-3),(3x-7) are acute angles

so

(2x-3)+(3x-7)=90

5x-10=90

5x=90+10

5x=100

x=20

2(20)-3=37

3(20)-7=53

so

37 is the smallest angle

Answer 2

The measure of the smallest angle in the triangle is 37°

Step-by-step explanation:

The measure of the acute angles of a right triangle are (2x -3) and (3x-7).

since ,

sum of all the angles of the triangle = 180°

(angle sum property)

It is given that it is a right triangle  i.e one angle must be 90°

therefore ,

taking $\angle C = 90$

$\angle A +\angle B +\angle C = 180$

(2x-3)+(3x-7)+90° = 180°

(2x-3)+(3x-7) = 180° - 90°

2x - 3+ 3x-7 = 90°

5x -10 = 90°

5x = 90 +10

5x = 100

x = $\frac{100}{5}$

x= 20°

now,

$\angle A$ = 2x-3 = 2(20)-3 = 40-3 = 37°

$\angle B$ = 3x-7 = 3(20)-7 = 60-7 = 53°

hence , $\angle A$ = 37° is the smallest angle in the triangle .

#Learn more:

In a right angle triangle,one of the acute angles measures 53°.find the measures of each angle of the triangle

https://brainly.in/question/5630530